I need a little more info here.
We are all perfectionist to some degree in our family of 4. DH and I are research scientists, ie, we found careers that required some degree of perfectionism and doggedness, attention to detail, and critical thinking skills.
So as long as it's not pushed to extremes, perfectionism is a personality trait like any other, it can give certain advantages in life, and should not be pathologized.
Instead of rushing to spend your money on a therapist, why don't you read up on perfectionism? Get a few books on the subject, and then make a plan to listen and talk with your daughter on an ongoing basis.
I would focus my conversation on economizing/prioritizing/sorting. These are all words to describe how a successful person channels their effort into what's most important to them and/or what is most likely to pay off in the long run to achieve their goal. Some teens are very good at this: to get all As without too much effort, they calculate exactly which assignment has the most weight and they need to do well on and which assignment they can just ignore
You might scoff at the example, but this is a key ability, because un-discriminating perfectionists and people-pleasers can end up with full-blown anxiety disorders because there comes a point in their lives when they have too much going on and they cannot succeed everywhere. They must learn to accept that failure in non-key areas can mean better success in critical areas.